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48
Determining Possible and Necessary Winners under Common Voting Rules Given Partial Orders
"... Usually a voting rule or correspondence requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a profile of part ..."
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Cited by 63 (13 self)
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Usually a voting rule or correspondence requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a profile of partial orders and a candidate c, two important questions arise: first, is c guaranteed to win, and second, is it still possible for c to win? These are the necessary winner and possible winner problems, respectively. We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We prove that for Copeland, maximin, Bucklin, and ranked pairs, the possible winner problem is NPcomplete; also, we give a sufficient condition on scoring rules for the possible winner problem to be NPcomplete (Borda satisfies this condition). We also prove that for Copeland and ranked pairs, the necessary winner problem is coNPcomplete. All the hardness results hold even when the number of undetermined pairs in each vote is no more than a constant. We also present polynomialtime algorithms for the necessary winner problem for scoring rules, maximin, and Bucklin.
AI’s war on manipulation: Are we winning?
 AI MAGAZINE
"... We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections. ..."
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Cited by 53 (8 self)
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We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections.
The shield that never was: Societies with singlepeaked preferences are more open to manipulation and control
 In Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge
, 2009
"... Much work has been devoted, during the past twenty years, to using complexity to protect elections from manipulation and control. Many results have been obtained showing NPhardness shields, and recently there has been much focus on whether such worstcase hardness protections can be bypassed by fre ..."
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Cited by 40 (14 self)
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Much work has been devoted, during the past twenty years, to using complexity to protect elections from manipulation and control. Many results have been obtained showing NPhardness shields, and recently there has been much focus on whether such worstcase hardness protections can be bypassed by frequently correct heuristics or by approximations. This paper takes a very different approach: We argue that when electorates follow the canonical political science model of societal preferences the complexity shield never existed in the first place. In particular, we show that for electorates having singlepeaked preferences, many existing NPhardness results on manipulation and control evaporate. 1
Eliciting singlepeaked preferences using comparison queries
 In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems
, 2007
"... Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to ..."
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Cited by 38 (5 self)
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Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to simply ask agents to report their complete preferences. Rather, the agents’ preferences, or at least the relevant parts thereof, need to be elicited. This is done by asking the agents a (hopefully small) number of simple queries about their preferences, such as comparison queries, which ask an agent to compare two of the alternatives. Prior work on preference elicitation in voting has focused on the case of unrestricted preferences. It has been shown that in this setting, it is sometimes necessary to ask each agent (almost) as many queries as would be required to determine an arbitrary ranking of the alternatives. In contrast, in this paper, we focus on singlepeaked preferences. We show that such preferences can be elicited using only a linear number of comparison queries, if either the order with respect to which preferences are singlepeaked is known, or at least one other agent’s complete preferences are known. We show that using a sublinear number of queries does not suffice. We also consider the case of cardinally singlepeaked preferences. For this case, we show that if the alternatives ’ cardinal positions are known, then an agent’s preferences can be elicited using only a logarithmic number of queries; however, we also show that if the cardinal positions are not known, then a sublinear number of queries does not suffice. We present experimental results for all elicitation algorithms. We also consider the problem of only eliciting enough information to determine the aggregate ranking, and show that even for this more modest objective, a sublinear number of queries per agent does not suffice for known ordinal or unknown cardinal positions. Finally, we discuss whether and how these techniques can be applied when preferences are almost singlepeaked. 1 1
Bypassing Combinatorial Protections: PolynomialTime Algorithms for Singlepeaked Electorates
, 2010
"... For many election systems, bribery (and related) attacks have been shown NPhard using constructions on combinatorially rich structures such as partitions and covers. It is important to learn how robust these hardness protection results are, in order to find whether they can be relied on in practice ..."
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Cited by 36 (5 self)
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For many election systems, bribery (and related) attacks have been shown NPhard using constructions on combinatorially rich structures such as partitions and covers. It is important to learn how robust these hardness protection results are, in order to find whether they can be relied on in practice. This paper shows that for voters who follow the most central politicalscience model of electorates—singlepeaked preferences—those protections vanish. By using singlepeaked preferences to simplify combinatorial covering challenges, we show that NPhard bribery problems—including those for Kemeny and Llull elections—fall to polynomial time. By using singlepeaked preferences to simplify combinatorial partition challenges, we show that NPhard partitionofvoters problems fall to polynomial time. We furthermore show that for singlepeaked electorates, the winner problems for Dodgson and Kemeny elections, though Θ p 2complete in the general case, fall to polynomial time. And we completely classify the complexity of weighted coalition manipulation for scoring protocols in singlepeaked electorates.
A Multivariate Complexity Analysis of Determining Possible Winners Given Incomplete Votes
"... The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes are extended into complete ones in a favorable way. POSSIBLE WINNER is NPcomplete for common voting rules such as Borda, many other positional scoring rules, Bu ..."
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Cited by 35 (9 self)
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The POSSIBLE WINNER problem asks whether some distinguished candidate may become the winner of an election when the given incomplete votes are extended into complete ones in a favorable way. POSSIBLE WINNER is NPcomplete for common voting rules such as Borda, many other positional scoring rules, Bucklin, Copeland etc. We investigate how three different parameterizations influence the computational complexity of POSSIBLE WINNER for a number of voting rules. We show fixedparameter tractability results with respect to the parameter “number of candidates ” but intractability results with respect to the parameter “number of votes”. Finally, we derive fixedparameter tractability results with respect to the parameter “total number of undetermined candidate pairs ” and identify an interesting polynomialtime solvable special case for Borda. 1
Swap bribery
, 2009
"... Abstract. In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of chang ..."
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Cited by 29 (12 self)
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Abstract. In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that the voter is asked to implement. Specifically, in our model the briber can change a voter’s preference list by paying for a sequence of swaps of consecutive candidates. Each swap may have a different price; the price of a bribery is the sum of the prices of all swaps that it involves. We prove complexity results for this model, which we call swap bribery, for a broad class of voting rules, including variants of approval and kapproval, Borda, Copeland, and maximin. 1
A Maximum Likelihood Approach towards Aggregating Partial Orders
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... In many of the possible applications as well as the theoretical models of computational social choice, the agents ’ preferences are represented as partial orders. In this paper, we extend the maximum likelihood approach for defining “optimal ” voting rules to this setting. We consider distributions ..."
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Cited by 22 (10 self)
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In many of the possible applications as well as the theoretical models of computational social choice, the agents ’ preferences are represented as partial orders. In this paper, we extend the maximum likelihood approach for defining “optimal ” voting rules to this setting. We consider distributions in which the pairwise comparisons/incomparabilities between alternatives are drawn i.i.d. We call such models pairwiseindependent models and show that they correspond to a class of voting rules that we call pairwise scoring rules. This generalizes rules such as Kemeny and Borda. Moreover, we show that Borda is the only pairwise scoring rule that satisfies neutrality, when the outcome space is the set of all alternatives. We then study which voting rules defined for linear orders can be extended to partial orders via our MLE model. We show that any weakly neutral outcome scoring rule (including any ranking/candidate scoring rule) based on the weighted majority graph can be represented as the MLE of a weakly neutral pairwiseindependent model. Therefore, all such rules admit natural extensions to profiles of partial orders. Finally, we propose a specific MLE model πk for generating a set of k winning alternatives, and study the computational complexity of winner determination for the MLE of πk.
Practical voting rules with partial information
 AUTON AGENT MULTIAGENT SYST
, 2010
"... Voting is an essential mechanism that allows multiple agents to reach a joint decision. The joint decision, representing a function over the preferences of all agents, is the winner among all possible (candidate) decisions. To compute the winning candidate, previous work has typically assumed that ..."
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Cited by 20 (4 self)
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Voting is an essential mechanism that allows multiple agents to reach a joint decision. The joint decision, representing a function over the preferences of all agents, is the winner among all possible (candidate) decisions. To compute the winning candidate, previous work has typically assumed that voters send their complete set of preferences for computation, and in fact this has been shown to be required in the worst case. However, in practice, it may be infeasible for all agents to send a complete set of preferences due to communication limitations and willingness to keep as much information private as possible. The goal of this paper is to empirically evaluate algorithms to reduce communication on various sets of experiments. Accordingly, we propose an iterative algorithm that allows the agents to send only part of their preferences, incrementally. Experiments with simulated and realworld data show that this algorithm results in an average of 35 % savings in communications, while guaranteeing that the actual winning candidate is revealed. A second algorithm applies a greedy heuristic to save up to 90 % of communications. While this heuristic algorithm cannot guarantee that a true winning candidate is found, we show that in practice, close approximations are obtained.